(10) Let f RR be the function given by f(x) = e and g (1,7) →R be given by g(x) = tan x. (a) Is fog injective? If no, can we restrict either the domain of f or g so that fog is surjective? (b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog is surjective? (c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range) of or g, so that fog is bijective?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 56E
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(10) Let f RR be the function given by f(x)
g(x) = tan x.
= e* and g : (-) → R be given by
(a) Is fo g injective? If no, can we restrict either the domain of f or g so that fog is
surjective?
(b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog
is surjective?
(c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range)
of f or g, so that fog is bijective?
Transcribed Image Text:(10) Let f RR be the function given by f(x) g(x) = tan x. = e* and g : (-) → R be given by (a) Is fo g injective? If no, can we restrict either the domain of f or g so that fog is surjective? (b) Is fog surjective? If no, can we restrict either the image (range) of f or g so that fog is surjective? (c) Is fog bijective? If no, can we restrict either the domain of f or g, or the image (range) of f or g, so that fog is bijective?
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